Just How Small Is the Proton?

Physicists have been scratching their heads since July, when a research team announced that the proton, the basic building block of matter, is 4 percent smaller than previously thought. The finding, published in Nature, clashes with theoretical predictions based on quantum electrodynamics, or QED, the fundamental theory of the electromagnetic force that had passed the most stringent tests in physics.

Randolf Pohl of the Max Planck Institute for Quantum Op­tics in Garching, Germany, and his collaborators used a laser to probe exotic, man-made hydrogen atoms in which elementary particles known as muons replaced the usual electrons orbiting the single-proton nuclei. Laser energy made the atoms fluoresce at char­acteristic x-ray wavelengths. Those wavelengths reflected a number of subtle effects, including the little known fact that an orbiting particle—be it a muon or an electron—often flies straight through the proton. That is possible because protons are composed of smaller elementary particles (mainly three quarks), and most of the space inside a proton is actually empty.

By calculating the effects of the proton’s radius on such fly-through trajectories, the researchers were able to estimate the proton’s radius to be 0.84184 femtometer (one femtometer is one quadrillionth of a meter). This figure is smaller than all previous measurements made, which ranged between 0.8768 and 0.897 femtometer. (Either way, the proton is a lot smaller than even a hydrogen atom: if the atom were the size of a football field, the proton would be the size of an ant.)

In dealing with such tiny quantities, the possibility for error always exists. Yet after 12 years of painstaking efforts (“You need to be stubborn,” Pohl says), the team members are confident that some unforeseen subtlety in their apparatus hasn’t thrown off their measurement. Theorists have also double-checked the calculations involved in interpreting the muons’ behavior and predicting the size of the proton, which are relatively straightforward, says Ulrich D. Jen­tschura, a theorist at the Missouri University of Science and Technology in Rolla.

Some physicists have suggested that the interaction between the muons and the proton could be complicated by unforeseen pairs of particles and their antiparticles, which might appear briefly from the vacuum in and around the nucleus. The most likely candidates, Jentschura says, are electron-antielectron pairs, which are not supposed to show up in the everyday physics of atoms, at least not according to the standard theory. “It could be the first indication that something is wrong with our picture” of QED, says Krzysztof Pachucki, a theorist at the University of Warsaw in Poland. The theory might need some tweaking, but likely not a complete overhaul, he says. Whatever the answer, physicists will most likely have plenty to keep scratching their heads about for years to come.